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  • Question
  • Four dice are thrown simultaneously. Find the probability that two of them show the same face and remaining two show the different faces.


  • Options
  • A. 4/9
  • B. 5/9
  • C. 11/18
  • D. 7/9

  • Correct Answer
  • 5/9 

    Explanation

    Select a number which ocurs on two dice out of six numbers (1, 2, 3, 4, 5, 6). This can be done in  C 1 6 , ways.

     

    Now select two distinct number out of remaining 5 numbers which can be done in  C 2 5  ways. Thus these 4 numbers can be arranged in 4!/2! ways.

     

    So, the number of ways in which two dice show the same face and the remaining two show different faces is 

      C 1 6 × C 2 5 × 4 ! 2 ! = 720

     =>  n(E) = 720

      ? P E = 720 6 4 = 5 9


  • Probability problems


    Search Results


    • 1. Two dice are rolled simultaneously. Find the probability of getting a total of 9.

    • Options
    • A. 1/3
    • B. 1/9
    • C. 8/9
    • D. 9/10
    • Discuss
    • 2. A group of five persons is formed from five boys and four girls. Find the probability that there are at least two girls in the group?

    • Options
    • A. 110/129
    • B. 5/6
    • C. 121/126
    • D. 3/7
    • Discuss
    • 3. In a simultaneous throw of two dice, what is the probability of getting a doublet ?

    • Options
    • A. 1/6
    • B. 1/3
    • C. 4/7
    • D. 4/5
    • Discuss
    • 4. In a party there are 5 couples. Out of them 5 people are chosen at random. Find the probability that there are at the least two couples ?

    • Options
    • A. 6/7
    • B. 19/21
    • C. 7/31
    • D. 5/21
    • Discuss
    • 5. If two dice are thrown together, the probability of getting an even number on one die and an odd number on the other is ?

    • Options
    • A. 1
    • B. 1/2
    • C. 0
    • D. 3/5
    • Discuss
    • 6. A box contains 5 detective and 15 non-detective bulbs. Two bulbs are chosen at random. Find the probability that both the bulbs are non-defective.

    • Options
    • A. 5/19
    • B. 3/20
    • C. 21/38
    • D. None of these
    • Discuss
    • 7. The letters of the word CASTIGATION is arranged in different ways randomly. What is the chance that vowels occupy the even places ?

    • Options
    • A. 0.04
    • B. 0.043
    • C. 0.047
    • D. 0.05
    • Discuss
    • 8. In a throw of a coin, find the probability of getting a head.

    • Options
    • A. 1
    • B. 1/2
    • C. 1/4
    • D. 0.1
    • Discuss
    • 9. A box contains 100 balls, numbered from 1 to 100. If three balls are selected at random and with replacement from the box, what is the probability that the sum of the three numbers on the balls selected from the box will be odd?

    • Options
    • A. 1/6
    • B. 1/3
    • C. 1/2
    • D. 1/4
    • Discuss
    • 10. A number is selected at random from the numbers 1 to 30. What is the probability that it is divisible by either 3 or 7 ?

    • Options
    • A. 1/30
    • B. 2/30
    • C. 1/25
    • D. 1/2
    • Discuss


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